This question is incomplete, the complete question is;
A general reaction written as A + 2B → C + 2D is studied and yields the following rate law: ∆A/∆t = k A².
The initial concentration is 1.000 M and t½=20.00 s.
How long will it take for the concentration to reach 0.0500 M
Answer:
it will take 380 seconds for the concentration to reach 0.0500 M
Explanation:
Given that;
A + 2B → C + 2D
initial concentration A₀ = 1 M
half life t1/2 = 20sec
concentration after t time [A_t] = 0.0500 M
∆A/∆t = k A²
This is a second order chemical kinetics
for this order; t1/2 = 1 / [A]₀K
A₀ is initial concentration, K is rate constant, t1/2 is half life
so,
k = 1 / [A₀]t1/2
we substitute
K = 1 / 1.000 × 20
K = 0.05 mol⁻¹L/sec
for second reaction order
1/[A_t] = kt + 1/[A₀]
kt = 1/[A_t] - 1/[A₀]
we substitute
kt = 1/0.0500 - 1/1.000
kt = 20 - 1
kt = 19
substitute the value of k
0.05 × t = 19
t = 19 / 0.05
t = 380 sec
Therefore it will take 380 seconds for the concentration to reach 0.0500 M